We estimate the maximum amount that Danish households are willing to
pay for three different types of insurance: auto, home and house insurance. We use a
unique combination of claims data from the largest private insurance company in
Denmark, measures of individual risk attitudes and discount rates from a field
experiment with a representative sample of the adult Danish population, and
information on household income and wealth from registers at Statistics Denmark.
We assume that households maximize expected inter-temporal utility subject to an
inter-temporal budget constraint with several possible states of nature, where all
uncertainty is realized in the initial period and any loss incurred by an accident is
subtracted from initial wealth. The estimated willingness to pay is based on annual
claims and should thus be considered as an annual premium. Since there is some
uncertainty about the estimates of risk attitudes and discount rates, there is some
uncertainty about the estimated willingness to pay. We use a randomized factorial
design in our sensitivity analysis where each simulation involves a random draw from
independent normal distributions of the estimated risk and time preferences. The
results show that the willingness to pay is marginally higher than the actuarial fair
value under Expected Utility Theory. However, the estimated willingness to pay is
significantly higher under Rank-Dependent Utility Theory, and for some households
it may be up to 600% higher than the actuarial value of the insurance claims.